Projecting interval uncertainty through the discrete Fourier transform: An application to time signals with poor precision

The discrete Fourier transform (DFT) is often used to decompose a signal into finite number of harmonic components. efficient and rigorous propagation the error present in through can be computationally challenging. Real data always subject imprecision because measurement uncertainty. For example, such uncertainty may come from sensors whose precision affected by degradation, or simply digitisation. On many occasions, only bounds on known, thus it necessary automatically propagate without making additional artificial assumptions. This paper presents method that interval DFT while yielding exact amplitude an estimation Power Spectral Density (PSD) function. allows technical analysts project – time signals PSD function assumptions about dependence distribution over steps. Thus, possible calculate analyse system responses frequency domain conducting extensive Monte Carlo simulations nor running expensive optimisations domain. applicability this practice demonstrated application. It also shown conventional methods severely underestimate